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  1. Home
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  4. Construction of cubature formula for double integration with algebraic singularity by spline polynomial
 
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Construction of cubature formula for double integration with algebraic singularity by spline polynomial

Journal
ICREM7 2015 - Proceedings of the 7th International Conference on Research and Education in Mathematics: Empowering Mathematical Sciences through Research and Education
Date Issued
2015
Author(s)
Bichi S.L.
Eshkuvatov Z.K.
Long N.M.A.N.
Ismail F.
DOI
10.1109/ICREM.2015.7357052
Abstract
In this note, singular integration problems of the form H? (h) = ??? h(x,y)/|-x0|2-? dA, 0 ? ? ? 1, where ? = [x0,y0] � [b1, b2], x= (x,y) ? ? and fixed point x 0 = (x0,y0) ? ? is considered. The density function h(x, y) is assumed given, continuous and smooth on the rectangle ? and belong to the class of functions C2,?(?). Cubature formula for double integrals with algebraic singularity on a rectangle is constructed using the modified spline function S?(P) of type (0, 2). Highly accurate numerical results for the proposed method is given for both tested density function h(x, y) as linear, quadratic and absolute value functions. The results are in line with the theoretical findings. � 2015 IEEE.
Subjects

Numerical methods

Absolute values

Cubature formula

Double integrals

Double-integration

Fixed points

Highly accurate

Integration problems

Spline functions

Algebra

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